A business owner wants to know if it will be profitable to open a new coffee shop in a nearby town.In towns where the shop has been successful,the shop name is recognizable to people 53% of the time .He survey random sample of 12 residents of the town

Complete question :

A business owner wants to know if it will be profitable to open a new coffee shop in a nearby town.In towns where the shop has been successful,the shop name is recognizable to people 53% of the time .He survey random sample of 12 residents of the town.  Find the probability that among these 12 surveyed residents, none of them have ever heard of the coffee shop

0.000116

Step-by-step explanation:

Using the binomial probability relation :

Probability of success, p = 0.53

1 - p = 0.47

Number surveyed, n = 12

P(x =x) = nCx  * p^x * (1 - p)^(n - x)

Probability that none has heard of the coffee shop :

P(x = 0) = 12C0 * 0.53^0 * 0.47^12

P(x = 0) = 0.000116